Decremental strongly-connected components and single-source reachability in near-linear time

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

Computing the Strongly-Connected Components (SCCs) in a graph G = (V, E) is known to take only O(m + n) time using an algorithm by Tarjan from 1972[SICOMP 72] where m = |E|, n = |V |. For fully-dynamic graphs, conditional lower bounds provide evidence that the update time cannot be improved by polynomial factors over recomputing the SCCs from scratch after every update. Nevertheless, substantial progress has been made to find algorithms with fast update time for decremental graphs, i.e. graphs that undergo edge deletions. In this paper, we present the first algorithm for general decremental graphs that maintains the SCCs in total update time Õ(m)1, thus only a polylogarithmic factor from the optimal running time. Previously such a result was only known for the special case of planar graphs [Italiano et al, STOC 17]. Our result should be compared to the formerly best algorithm for general graphs achieving Õ(mn) total update time by Chechik [FOCS 16] which improved upon a breakthrough result leading to O(mn0.9+o(1)) total update time by Henzinger, Krinninger and Nanongkai [STOC 14, ICALP 15]; these results in turn improved upon the longstanding bound of O(mn) by Roditty and Zwick [STOC 04]. All of the above results also apply to the decremental Single-Source Reachability (SSR) problem, which can be reduced to decrementally maintaining SCCs. A bound of O(mn) total update time for decremental SSR was established already in 1981 by Even and Shiloach [JACM 81].

TitelSTOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
RedaktørerMoses Charikar, Edith Cohen
Antal sider12
ForlagAssociation for Computing Machinery
ISBN (Elektronisk)9781450367059
StatusUdgivet - 2019
Begivenhed51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, USA
Varighed: 23 jun. 201926 jun. 2019


Konference51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019
NavnProceedings of the Annual ACM Symposium on Theory of Computing

ID: 239207274